A075055 Smallest integer of the form product (n+1)(n+2)...(n+k)/n!.

1, 1, 6, 20, 70, 252, 7, 3432, 12870, 48620, 184756, 705432, 2704156, 10400600, 40116600, 178296, 601080390, 2333606220, 9075135300, 35345263800, 137846528820, 538257874440, 2104098963720, 8233430727600, 32247603683100, 126410606437752, 495918532948104

Offset

0,3

Comments

Differs from A000984 at positions in A058008.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1664

Example

a(6) = 7 = 7*8*9*10/6! = 5040/720.

Maple

a:= proc(n) option remember; local k, t; t:= 1/n!;
      for k while denom(t)>1 do t:= t*(n+k) od; t
    end:
seq(a(n), n=0..28);  # Alois P. Heinz, Feb 05 2025

Mathematica

a[n_] := Catch[ For[ k = n-2, True, k++, If[ IntegerQ[an = (n+k)!/n!^2], Throw[an]]]]; a[1]=1; Table[a[n], {n, 1, 24}] (* Jean-François Alcover, Jun 28 2012 *)

Crossrefs

Cf. A075054.

Sequence in context: A264307 A050930 A074353 * A146891 A235367 A189604

Adjacent sequences: A075052 A075053 A075054 * A075056 A075057 A075058

Keyword

nice,nonn

Author

Amarnath Murthy, Sep 07 2002

Extensions

More terms from Sascha Kurz, Feb 02 2003

a(0)=1 prepended by Alois P. Heinz, Feb 05 2025

Status

approved